Not entirely sure if asking this issue here is reasonable, but I have had the issue for nearly a year and just now got around to it. It will be helpful to know my car has previous accident history, the front end was damaged. This issue did not appear when we first got the car. I own a 2008 BMW 135i E88 and every time I accelerate and try to keep it below 2 1/2 RPMs, I can get a violent vibration you can feel throughout the whole cabin with an occasional sound of a chain. RPMs also fluctuate where they do not go upward smoothy while instead ticking up which is a weird look. However, if you step on the pedal harder, the vibration is nearly nonexistent. I took my car to BMW and paid to get a diagnosis, in which they basically said they didn't know and to pay to have my engine coils/spark plugs replaced then pay more money to have my transmission to be worked on if that didn't solve the issue. We did our engine coils/spark plugs ourselves and that did not resolve the issue. There have been wheel alignments and balances off and on, with OEM wheels/tires and with my aftermarket wheels/tires. Suggestions?
Video of my experience, although it can get worse;